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dc.contributorMolina Blanco, Santiago
dc.contributor.authorFelipe i Alsina, Marc
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractIn this thesis, we take a look into a generalization of Local Class Field Theory (LCFT), called the Local Langlands Conjecture, which concerns about identifying special representations of the Weil group, a subgroup of the absolute Galois group of a field, with some representations of the general linear group with coefficients in that field. We study deeply the $n=1$ case, which corresponds to LCFT, and then we construct explicit elements of both sides of the bijection for the case $n=2$. Finally, we state the difficulties to formulate the analogous conjecture for global fields, the Global Langlands Conjecture.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
dc.subject.lcshAlgebraic number theory
dc.subject.otherLanglands program
dc.subject.otherNumber theory
dc.subject.otherAutomorphic forms
dc.subject.otherLocal class field theory
dc.titleAn introduction to the Langlands Conjectures
dc.typeMaster thesis
dc.subject.lemacCossos locals (Geometria algèbrica)
dc.subject.lemacNombres, Teoria algebraica de
dc.subject.amsClassificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields
dc.rights.accessRestricted access - author's decision
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

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